Can I sue an airline for losing my baggage?

In theory you can. However, you say you entered the US from overseas. Did you check the ticket? Did you buy a travel insurance? If so, what does the contract say about the maximum value of repayment in case of lost baggage? Some airline companies provide a flat amount for reimbursement of lost luggage. You can try to simply contact the claim office of your airline company and discuss your options. On the other side, if you can prove (with evidence) that you were travelling with precious and expensive goods in your luggage you may again theoretically sue. But then you may have another problem: did you report to US Customs what you were transporting? Based on your facts, I would encourage you to hire an attorney in your area. Good luck.

If your international flight originated in the country - signatory to the Montreal Convention (MC) (which exclusively governs liability of airline to passenger resulting from international carriage of passengers and their luggage), than pursuant to art. 19 and 22 of MC an airline is strictly liable for loss of your luggage up to the sum of 1131 SDR (approximately $1750). Importantly, if the Montreal Convention applies, any conditions on the contrary as possibly imposed by an airline are not enforceable because effect of strict liability regime under MC cannot be altered by an airline. If the MC does not apply, than you can recover from an airline entire value of your lost luggage on international flight. (On domestic flights liability of airline is limited by the sum of $3300 pursuant to 42 C.F.R. 250 -253.4). Therefore, an airline will most likely offer to you the settlement without any court action, and you can get a maximum sum of $1750 if you will substantiate your claim with receipts showing value of contents of your lost belongings. Good luck.